Due the school day after we cover the lesson in class
8-1: Chris K. and Jared K.
8-2: Tarah L. and Kortnee M.
8-3: Ben B. and Alyssa M.
8-4: Alexis H. (Bonus) and Ben R. (Bonus)
8-5: Nick C. and Stephanie G.
8-6: Derrik B. and Erica M.
8-7: Ben B. and Isaac H.
Student Summaries: Section 8-2 by Kortnee M.
This lesson shows us how to determine if an ordered pair is a solution of a system, and how you solve a system of liner equations graphically. We can determine if an ordered pair is a solution by putting the ordered pair we have into both of the equations. If the equations are true the ordered pair is a solution or possibly where they intercept.
By graphing you put the equations into slope intercept form. Next step is to graph the equation, like in the earlier lessons. The lines will either intercept or be parallel. The lines will be parallel if they have the same slope. If the slopes equal a -1 then the lines will be parallel.
Tarah L.
This lesson teaches about the way to discover if a specific ordered pair is a solution of a system & how to solve systems of linear equations graphically. The systems of equations are two or more equations with the same two variables that you solve at the same time. The solution of a system if considered the intersection of the two lines, which is also the ordered pair that makes both equations true. To find out if an ordered pair is a solution to a system, you plug in the ordered pair to each equation of the system & see if they both equal the same number. If the system of equations are not in slope-intercept form then they must be simplified to this before plugging in the ordered pair. To solve systems of linear equations graphically, first you put the equations in slope-intercept form, if they're not already. Then you graph both equations on the coordinate plane & if they both intersect at the same ordered pair, then this would be the solution. To make sure this ordered pair is correct though, it is a good idea to check it by plugging it into both of the equations.
Student Summaries:
Okay, so in Chapter 8-3 we learned about Solving Systems by Substitution. Basically, all this mean is if you have a variable equation you plug in the value of the variable given to find the other variable. If there is no variable given to you then you have to solve for one of the two variables and then plug in that variable into the other equation to find the other variable. Once you have found both of your variables you have to put them into an ordered pair to show the spot at where the points meet. This is called a coordinate pair. After you have found your coordinate pair what you want to do finally is check your work. You do this plugging the numbers from your coordinate pair back into one of the original two equations. If everything works out than you know that you are right. If it does not work out than just simply go back and check over some of your work to check for an error. - Ben B.
8-4: Solve Systems by Adding, Subtracting, and Multiplying
Student Summaries:
Ben R.:
This Lesson involes us solving equation by using the operations such as addition, subtraction, and multiplying or known as linear combinations. You may also see this in areas landscaping, and sports. this will involve you to graph with accuracy. Also subitution and combination. We solve problems by picking the easiest problem out of the two, then you find the missing variable as you do this you will eventually have to subsitute your answer into the second equation to get you final answer. But for the last step you will have to go back and check all of you work by working backwards. This concluding the step-by-step in linear combinations.
Alexis H.
This lesson has addition, subtraction, and multiplying. There is also subitution and combination. This lesson helps you from day to day life in landscaping and many other things. always remember to check your work by working backwards and always check your work
Student Summaries: Stephanie & Nick: The most important thing to know in 8-5 is making sure your equations are in Ax+By=C form, which is called Cramer's Rule. When you are using a square matrix (2X2)(same number of rows and colums), all you do to find the determinate from the matrix is use the formula det A=ad-bc. Then you'll find the determinate.
Student Summaries:Derrik B. Lesson 8-6 talks about Problem solving skills: Directed Graphs. A directed graph is a geometrical representation of a map. You can use a directed graph when using different airlines and the ways they travel from one destination to another. However, before you make your directed graph with whatever information that is given to you, it is always good to make a matrix (size will vary depending on situation) to make sure your information is accurate.
Student Summaries:
When you have linear inequalities the first step you take to solve them is to graph them on separate coordinates, and then again on the same coordinates. You do this by marking your points onto the graph for each inequality. After you have them points plotted then depending on if the inequality sign is grater than or less than, or grater than or equal to or less than or equal to, you either connect your dots with a solid or a dotted line. If the sign is less than or greater than the line will be dotted. If the sign is less than or equal to or greater than or equal to then the line will be solid. After you have both your lines graphed you should find out what way you are going to be shading for both lines. The shaded area that overlaps represents the solutions of the systems of inequalities. - Ben B.
Table of Contents
Chapter 8: Systems of Equations and Inequalities
Preview: Chapter 8 Preview 0910.pdfWiki Summary Assignments
Due the school day after we cover the lesson in class8-1: Chris K. and Jared K.
8-2: Tarah L. and Kortnee M.
8-3: Ben B. and Alyssa M.
8-4: Alexis H. (Bonus) and Ben R. (Bonus)
8-5: Nick C. and Stephanie G.
8-6: Derrik B. and Erica M.
8-7: Ben B. and Isaac H.
8-1: Parallel and Perpendicular Lines
Notes: Section 8-1 Student 0910.pdfView a lesson summary here
Summary on iTunes
Student Summaries:
8-2: Solving Systems of Equations Graphically
Notes: Section 8-2 Student 0910.pdfView a lesson summary here
Summary on iTunes
Student Summaries:
Section 8-2 by Kortnee M.
This lesson shows us how to determine if an ordered pair is a solution of a system, and how you solve a system of liner equations graphically. We can determine if an ordered pair is a solution by putting the ordered pair we have into both of the equations. If the equations are true the ordered pair is a solution or possibly where they intercept.
By graphing you put the equations into slope intercept form. Next step is to graph the equation, like in the earlier lessons. The lines will either intercept or be parallel. The lines will be parallel if they have the same slope. If the slopes equal a -1 then the lines will be parallel.
Tarah L.
This lesson teaches about the way to discover if a specific ordered pair is a solution of a system & how to solve systems of linear equations graphically. The systems of equations are two or more equations with the same two variables that you solve at the same time. The solution of a system if considered the intersection of the two lines, which is also the ordered pair that makes both equations true. To find out if an ordered pair is a solution to a system, you plug in the ordered pair to each equation of the system & see if they both equal the same number. If the system of equations are not in slope-intercept form then they must be simplified to this before plugging in the ordered pair. To solve systems of linear equations graphically, first you put the equations in slope-intercept form, if they're not already. Then you graph both equations on the coordinate plane & if they both intersect at the same ordered pair, then this would be the solution. To make sure this ordered pair is correct though, it is a good idea to check it by plugging it into both of the equations.
8-3: Solve Systems by Substitution
Notes: Section 8-3 Student 0910.pdfView a lesson summary here
Summary on iTunes
Student Summaries:
Okay, so in Chapter 8-3 we learned about Solving Systems by Substitution. Basically, all this mean is if you have a variable equation you plug in the value of the variable given to find the other variable. If there is no variable given to you then you have to solve for one of the two variables and then plug in that variable into the other equation to find the other variable. Once you have found both of your variables you have to put them into an ordered pair to show the spot at where the points meet. This is called a coordinate pair. After you have found your coordinate pair what you want to do finally is check your work. You do this plugging the numbers from your coordinate pair back into one of the original two equations. If everything works out than you know that you are right. If it does not work out than just simply go back and check over some of your work to check for an error. - Ben B.
8-4: Solve Systems by Adding, Subtracting, and Multiplying
Notes: Section 8-4 Student 0910.pdfView a lesson summary here
Summary on iTunes
Student Summaries:
Ben R.:
This Lesson involes us solving equation by using the operations such as addition, subtraction, and multiplying or known as linear combinations. You may also see this in areas landscaping, and sports. this will involve you to graph with accuracy. Also subitution and combination. We solve problems by picking the easiest problem out of the two, then you find the missing variable as you do this you will eventually have to subsitute your answer into the second equation to get you final answer. But for the last step you will have to go back and check all of you work by working backwards. This concluding the step-by-step in linear combinations.
Alexis H.
This lesson has addition, subtraction, and multiplying. There is also subitution and combination. This lesson helps you from day to day life in landscaping and many other things. always remember to check your work by working backwards and always check your work
8-5: Matrices and Determinants
Notes: Section 8-5 Student 0910.pdfView a lesson summary here
Summary on iTunes
Student Summaries:
Stephanie & Nick: The most important thing to know in 8-5 is making sure your equations are in Ax+By=C form, which is called Cramer's Rule. When you are using a square matrix (2X2)(same number of rows and colums), all you do to find the determinate from the matrix is use the formula det A=ad-bc. Then you'll find the determinate.
8-6: Directed Graphs
Notes: Section 8-6 Student 0910.pdfView a lesson summary here
Summary on iTunes
Student Summaries:Derrik B. Lesson 8-6 talks about Problem solving skills: Directed Graphs. A directed graph is a geometrical representation of a map. You can use a directed graph when using different airlines and the ways they travel from one destination to another. However, before you make your directed graph with whatever information that is given to you, it is always good to make a matrix (size will vary depending on situation) to make sure your information is accurate.
8-7: Systems of Inequalities
Notes: Section 8-7 Student 0910.pdfView a lesson summary here
Summary on iTunes
Student Summaries:
When you have linear inequalities the first step you take to solve them is to graph them on separate coordinates, and then again on the same coordinates. You do this by marking your points onto the graph for each inequality. After you have them points plotted then depending on if the inequality sign is grater than or less than, or grater than or equal to or less than or equal to, you either connect your dots with a solid or a dotted line. If the sign is less than or greater than the line will be dotted. If the sign is less than or equal to or greater than or equal to then the line will be solid. After you have both your lines graphed you should find out what way you are going to be shading for both lines. The shaded area that overlaps represents the solutions of the systems of inequalities. - Ben B.
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